Biochemistry 1984, 23, 3636-3648
3636
On the Origin of the Lactate Dehydrogenase Induced Rate Effect? John W. Burgner, II,* and William J. Ray, Jr.
ABSTRACT: To evaluate the ability of lactate dehydrogenase to facilitate the bond making/breaking steps for both the addition of pyruvate enol to NAD (pyruvate adduct reaction) and the normal redox reaction, the ability of the enzyme to facilitate the tautomerization of bound pyruvate is assessed. In addition, the equilibrium constants for the adduct reaction are obtained for both bound and free reactants from the ratio of the rate constants in the forward and reverse reactions (at pH 7). The latter comparison indicates that the enzyme facilitates bond making/breaking in the (forward) pyruvate adduct reaction by a factor of about 10" M. Similar comparisons suggest that reactant immobilization accounts for about 1000 M of this 10" M rate effect. Since the (pH-independent) rate constant for the ketonization of bound pyruvate enol assisted by the external buffer, imidazolium ion, is 2 X lo7 M-' s-I and the corresponding rate constant for free pyruvate enol, again assisted by imidazolium ion, is 35 M-' s-I [Burgner, J. W., 11, & Ray, W. J., Jr. (1978) Biochemisrry 17, 16641, the enzyme facilitates the bond making/breaking
steps associated with the conversion of bound HO-Cf to bound O=C< by a factor of about 106-fold. The product of the above two rate enhancement factors and the rate factor suggested previously for the environmental effect on NAD produced by its binding to lactate dehydrogenase, 100-fold, is 10" M, and it accounts for the bond making/breaking effects exerted by the enzyme in the pyruvate adduct reaction. The rate constant for oxidation of ethanol (a model for lactate) by 1-methylnicotinamide (a model for NAD) is about 5 X M-l s-' at 25 OC in pure ethanol (AZP for this reaction is about 30 kcal/mol). The ratio of the rate constants for E.NAD-Lac EmNADHOPyr and the above model reaction is estimated as about 1014M in water; Le., the LDH-induced rate effect is about l O I 4 M. The product of the values for the above rate factors for the normal redox reaction is about 10l2 M. Although the value of this product is less certain than that for the adduct reaction, these rate factors do account for much of the LDH-induced rate effect.
I n comparing enzymic and nonenzymic reactions, one must make a choice between comparing the efficiency of an enzyme in facilitating bond breaking/making and the efficiency of the enzyme as a catalyst. Thus, the efficiency of an enzyme in facilitating chemical transformations is reflected in the rate constant, k,, for a discrete bond breaking/making step, e.g., as in
interest, we concentrate on the ratio k,/k,, for the oxidation of lactate by NAD in the presence and absence of LDH.' To provide even a semiquantitative rationale for the large value for k,/k,, of about 1014M (see Discussion), the various factors that contribute to k, must be identified and evaluated. This is particularly difficult since alterations that probe the importance of one factor also may affect the contributions of others. But, there seems to be no alternative other than to proceed in this manner, and we proceed cautiously by using as many internal comparisons as possible. Previously, we suggested that the pyruvate adduct reaction is a useful model for studying the normal reaction for the following reasons. (1) Both reactants are substrates of the enzyme, although not the normal pair. (2) The same groups on the enzyme probably are involved in both reactions. (3) To a first approximation, the addition of the pyruvate enol (and/or the enolate) to NAD mimics the addition of the hydride ion to NAD. (4) The bond-making step in the enzymic adduct reaction actually is faster than the hydride-transfer step. ( 5 ) The enzyme is an efficient bond maker/breaker. In combination, these considerations suggest that providing a description for the basis of the large value of k,/k,, in the adduct reaction should provide a basis for explaining the somewhat larger value of k,/k,, in the normal redox reaction. Hence, this paper is the third in a series where nucleophilic additions to the 4 position of NAD bound to lactate de-
E-A-B A E.P.Q By contrast, its efficiency as a catalyst is reflected in kc,,/ (KiAKe),e.g., as in (En@
A+BP+Q Both of the above constants can be compared with the bimolecular rate constant, k,,, for the analogous uncatalyzed reaction. In most cases, the ratio of kat/(&&,) to k,, will be enormous because a substantial intrinsic binding energy is available to facilitate the enzymic reaction (Jencks, 1975, 1980). Part of this energy is used solely for binding, as in the case of phase-transfer catalysts [cf. Jones (1976)], and the remainder to facilitate bond making/breaking. On the other hand, the ratio k J k , reflects the intrinsic binding energy that is used during the bond making/breaking step(s). In fact, the basis of the transition-state binding paradigm is that noncovalent binding interactions are responsible for the large values of k,/ k,, that usually are observed. But, this paradigm is so all inclusive that it is not useful as a detailed molecular explanation of how intrinsic binding energy is used to accelerate bond making/breaking steps (Ray & Long, 1976). Since the mechanism for using intrinsic binding energy is our primary From the Department of Biological Sciences, Purdue University, West Lafayette, Indiana 47907. Received November 9, 1983. This investigation was supported by a research grant from the National Science Foundation (GB012576).
0006-2960/84/0423-3636$0 1.50/0
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'
Abbreviations: LDH, lactate dehydrogenase (the dogfish A4 isozyme unless otherwise specified); E.X, complex of LDH with X; PyrK,PyrE, and Pyre, the keto, enol, and enolate forms of pyruvate; NAD, nicotinamide adenine dinucleotide; APAD, 3-acetylpyridine adenine dinucleotide; NAD-Pyr and APAD-Pyr, the covalent adducts of pyruvate with NAD and APAD, K,, an equilibrium constant; K x , the dissociation constant for the complex E.X; NAD-Lac, a covalent complex of NAD and lactate where the methyl group of lactate is attached via a methylene bridge at the 5 position of the nicotinamide ring of NAD.
0 1984 American Chemical Societv
O N THE LDH-INDUCED RATE EFFECT
VOL. 23, NO. 16, 1984
3637
Scheme I
hydrogenase are examined in an attempt to evaluate those factors that contribute to the efficiency of the normal reaction. Previous studies also have established that an external buffer acts as a general catalyst during the pyruvate adduct reaction, that the step in the overall reaction subject to general catalysis is the pyruvate enol-keto tautomerization involving bound pyruvate, and that the rate of this step is accelerated significantly by the enzyme (Burgner & Ray, 1978, 1984b). This system provides a unique opportunity for estimating the importance of general catalysis in an enzymically catalyzed reaction. Because of the unexpectedly large rate enhancement observed for general catalysis, lo6 M (see Discussion), several of its aspects are compared and contrasted for the enzymic and nonenzymic processes. The various rate and equilibrium constants in the enzymic and nonenzymic adduct reactions involving pyruvate are shown in Scheme I, where the reactions are presented so that analogies with the normal enzymic reaction are maximized. This paper compares the two nonenzymic reactions in boldface type on the left-hand side of Scheme I with the analogous enzymic reactions in boldface type on the right. In these two reactions, the buffer-assisted ketonization of free PyrE (lower left) is compared with the buffer-assisted ketonization of enzymebound Pyre (lower right), and the formation of the bond between PyrE and NAD (upper left) is compared with the analogous process when both reactants are bound to the enzyme (upper right). Materials and Methods Most materials and assay procedures are described in previous papers (Burgner et al., 1978; Burgner & Ray, 1974, 1978, 1984a,b). Only dogfish A4 LDH is used in these experiments. The temperature for all assays unless otherwise noted is 15 OC,and the pH values for all buffers refer to the final assay conditions. When APAD is substituted for NAD, it is used at the same concentrations that were used previously for NAD. Spectral measurements are made in a Perkin-Elmer Model 57 5 spectrophotometer equipped with an electronic temperature controller; fluorescent measurements are made in an instrument described elsewhere (Burgner & Ray, 1978). The APAD-Pyr and APAD-acetone adducts are prepared in the absence of enzyme by dissolving 10 pmol of APAD and 100 pmol of either acetone or pyruvate into 1 mL of a solution containing equal volumes of dimethyl sulfoxide and 0.1 M sodium carbonate buffer, pH 11, and allowing the mixture to stand for 1 h at room temperature. l-Methyl-l,Cdihydronicotinamide was prepared by the method of Karrer & Blumer (1947), and its identity and purity were checked by NMR spectroscopy.
The stoichiometry of the APAD-Pyr enzyme complex was determined by using the quenching of enzymic fluorescence as an assay for bound adduct [cf. Burgner & Ray (1978)l. The adduct was prepared (see above) so that its final concentration was about 104-fold greater than that of the enzymic subunits, about 1.2 pM, and immediately prior to the addition, an aliquant of the stock adduct was diluted in ice-cold water so that 1-5 p L would give the desired concentration when added to the l-ml assay mixture. Each assay solution containing enzyme was used for only two additions of the adduct, and the enzyme was exposed to the adduct only for about 2 min. Other conditions are given in Figure 1. The rate and equilibrium position of the nonenzymic reactions of APAD and pyruvate are measured by following the appearance of the near-UV absorption band of APAD-Pyr at 350 nm. The reactions typically were initiated by adding a small aliquant of 1 M sodium pyruvate to the assay mixture. The reverse nonenzymic reaction was studied by diluting the adduct reaction mixture by 100-fold (initial pH 11) into a reaction mixture containing the appropriate buffer (lower pH). The disappearance of the near-UV absorbance band was followed. The reverse enzymic adduct reaction was examined either by addition of a 2-fold excess of APAD-Pyr to the enzyme at pH 7.0 or after removal of excess reactants (APAD and pyruvate) from an equilibrium mixture by rapid molecular sieving at 4 OC (Penefsky, 1977); see also Burgner & Ray (1984a). For inhibition studies, both product-time and initial velocity assays of the normal redox reaction in the presence of APAD-Pyr are initiated by adding the apoenzyme to the assay mixture immediately after adding the APAD-Pyr. The enzyme concentration was increased with increasing inhibitor concentration so that a measurable initial slope was obtained in all cases. Product-time data are analyzed either graphically, as described in Figure 2, or numerically, as in Burgner et al. (1978). The reduction of l-methylnicotinamide by "neat" ethanol, which was freshly dried over molecular-sieving beads (4 A), was detected by the change in absorbance at 340 nm as a function of time (0.2 absorbance scale; l-cm light path). A Teflon-stoppered cuvette, which was wrapped at the top with Parafilm, prevented the loss of solvent. To detect acetaldehyde, several test tubes containing 50 mg of l-methylnicotinamide plus 5 mL of freshly dried ethanol were frozen, evacuated, and sealed with a flame. One tube was stored in liquid nitrogen as a control. After 5 days at 55 OC, one tube was analyzed by gas chromatography (Westcott et al., 1980). The other four tubes were combined and flushed continuously with ni-
3638
BIOCHEMISTRY
BURGNER AND RAY
E f
0
a
Equivalents Added FIGURE 1: Titration of LDH with APAD-Pyr: equivalents of APAD-Pyr added per equivalent of active sites. The initial concentration of active sites was 1.25 (@) and 2.50 pM).( in 0.3 M imidazole hydrochloride pH 7.0. The titration was followed by the decrease in fluorescence of the enzyme and completed within 2 min to prevent a significant loss of APAD-Pyr. The percent saturation was calculated by Holbrook's method [cf. Burgner & Ray (1983b)l; the solid lines were drawn by eye.
trogen (while maintaining the solution at 21-22 "C), and the gas was passed through a cold trap equilibrated with liquid nitrogen. The presence of acetaldehyde in the trap was detected qualitatively by the change in absorbance at 340 nm on addition of an aliquant of the trapped material (in water) to an assay mixture containing 0.15mM NADH and 10 nM alcohol dehydrogenase in a phosphate buffer (pH 7 and 0.1 MI. Results The nonenzymic adduct reaction involving pyruvate and NAD is difficult to compare with the corresponding reaction catalyzed by LDH because the NAD-Pyr adduct cyclizes during the nonenzymic reaction (Ozols & Marinetti, 1969). Hence, the pyruvate adduct of acetylpyridine adenine dinucleotide, APAD, is substituted for the corresponding adduct of NAD in many comparisons because the former adduct does not cyclize. Differences produced by this substitution are compensated for by comparing adduct reactions of MAD and NAD where the product does not cyclize, e.g., reactions involving the addition of CN- or S032-. Stoichiometry of the EmAPALtPyr Complex. To demonstrate that the binding stoichiometry of APAD-Pyr and LDH is the same as that for NADH, both the decrease in enzymic fluorescence as a function of added APAD-Pyr and the amount of APAD-Pyr required to saturate the enzyme are measured. In Figure 1, the fractional saturation of the enzyme with APAD-Pyr is plotted against the moles of adduct added per mole of active sites. The horizontal intercept indicates an 8:1 equivalency between adduct and enzyme. Because the APAD-Pyr adduct is prepared nonenzymically (see Materials and Methods), an approximately equal distribution of A and B isomers of the adduct is present (Arnold & Kaplan, 1974), and the A isomer should bind much more tenaciously than its enantiomer. Hence, the observed 8:l equivalency is as expected when each subunit binds only one of the two adduct isomers. To demonstrate that only half of the chemically prepared adduct present at the equivalence point actually binds tightly to the enzyme, a rapid molecular-sieving technique was
40
80
120
Time, sec FIGURE2: Effect of APAD-Pyr on a product-time plot for the normal enzymic reaction (Pyr Lac). The initial concentrations of NADH, Pyr, and MAD-Pyr were 1.51 X lo4, 6 X lo4, and 14.4 X lo4 M, respectively, in 0.3 M imidazole hydrochloride, pH 7.0. The reaction N was initiated by adding enzyme to a concentration of 1.5 X sites. Curve A is a (semilog) plot of A3a against time. The dashed line represents the product-time course of the steady-state phase extrapolated back to zero time. Curve B is a (semilog) plot of the difference in the above two lines, A, as a function of time; koM =
-
0.04 s-l.
used to remove any unbound APAD-Pyr (see Materials and Methods). Since the enzyme is almost completely recovered (>95%) and since the absorbance at 340 nm is decreased 2-fold by the sieving procedure, the enzyme must bind only one of the two isomers present. Hence, the stoichiometry of APAD-Pyr binding is the same as that for the binding of NADH [cf. Holbrook et al. (1975)].2 Competitive Binding between APALl-Pyr and NADH. The linearity of the titration in Figure 1 up to nearly the equivalence point indicates the dissociation constant for the E. APAD-Pyr complex must be substantially less than the concentration of enzyme used in that titration: 1.25 pM. The dissociation constant for this complex was estimated by measuring the competitive binding between APAD-Pyr and NADH with a steady-state assay involving the normal redox reaction. The basis for this assay, which was described previously (Burgner et al., 1978), is shown in Figure 2, plot A. This product-time plot describes the disappearance of NADH during the reduction of pyruvate and occurs when the enzyme is added to an assay mixture containing 15 nM APAD-Pyr, half-saturating pyruvate, and saturating NADH. In the absence of APAD-Pyr, the product-time plot is linear with a slope identical with the initial slope in Figure 2. The initial burst of product prior to the steady state in the presence of 1-10 nM concentrations of APAD-Pyr is caused by the relatively slow formation of the steady-state level of the dead-end EmAPAD-Pyr complex, as is shown in the following section. A similar fluorometric titration also was attempted with the nonenzymically prepared NAD-Pyr adduct, since this adduct also inhibits the enzyme (Everse et al., 1971). However, no significant decrease in enzyme fluorescence was noted when 4 equiv (-4 nmol/mL) of this adduct was added to the enzyme. Since in the absence of enzyme the NAD-Pyr adduct undergoes an additional cyclization [cf. Everse et al. (1971)] that involves the a-carbon of the pyruvate moiety and the carboxamide nitrogen, this additional cyclization apparently reduces the strength of the binding interaction by a large factor.
VOL. 23, N O . 16, 1984
ON THE LDH-INDUCED RATE EFFECT [APNAD-PYR], 0
25
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nm 75 I
/ iJ" a W OI 0 J
[NADH] x
M"
3: Effect of APAD-Pyr on the steady-state velocity of the Lac). The conditions and assay pronormal L D H reaction (Pyr cedures are the same as those in Figure 2, except that the enzyme concentration was 7.5 n M for assays at 72 nM MAD-Pyr. The other conditions are shown on the graph. (Inset) A plot of the slopes of the lower plots against the inhibitor concentration; a value of 9 X 10-" M is calculated from the slope to intercept ratio of the inset plot by using the measured slope in the absence of APAD-Pyr as the intercept value in this ratio.
-2
-3
FIGURE
Time, min
-+
Scheme I1 E,H.APAD-Pyr
I
kof f
k,"
E + APAD-PYR
I
k?e
4 E C A P A O t Pf' y r
Hence, the slope of the dashed line in Figure 2 describes the velocity of the normal enzymic reaction after the steady-state level of E-APAD-Pyr is reached. Figure 3 shows a plot of the steady-state velocity against 1/ [NADH] in the presence and absence of APAD-Pyr; the concentrations shown are those for the adduct isomer that binds to LDH, Le., half the total adduct concentration. (These experiments are not designed to show that this adduct is competitive with NADH; i.e., an intersection of the lines in the third quandrant cannot be ruled out. In fact, the experimental design is dictated by both the slow, spontaneous decomposition of the inhibitor and its small dissociation constant-see below as well as the following section,) The inset of Figure 3 shows a replot of the slopes of the lines in the figure against the inhibitor concentration. The interceptjslope ratio of the replot, 9 X lo-" M, is the apparent inhibition constant for APAD-Pyr: GPP. [The vertical intercept in this replot is taken as the measured slope in the absence of inhibitor (not shown)-not the extrapolated value at [APNAD-Pyr] = 0 obtained from the regression intercept.J As is shown below, this apparent inhibition constant is nearly equal to t h e true dissociation constant Kd f o r t h e EeAPAD-Pyr complex even though the APAD-Pyr adduct can both dissociate from the enzyme and decompose while bound to the enzyme as well as decompose spontaneously when free in solution (cf. Scheme 11). Thus, in the present case, Gpp= (koff+ kdw)/ko,,,and Gppwill equal Kd when koff>> kd,. This inequality holds under the conditions used in Figure 3 for the E.H-APAD-Pyr complex but not for the E.H. NAD-Pyr complex where kdcc >> kofp3
Effect of enzyme concentration on course of the reverse adduct reaction at p H 7.0. In both reactions, the buffer was 0.3 M imidazole hydrochloride. For curve A, the assay initially contained 26 rN EqAPAD-Pyr and 1 M potassium oxalate; for curve B, the assay initially contained 9 X N E-APAD-Pyr (see text for additional details). The values of koW are 1.1 X lo4 s-' and 7 X lo4 s for curves A and B, respectively. The lines were drawn by eye. FIGURE 4:
The attachment of the pyruvate moiety to the 4 position of the pyridinium ring of APAD increases the strength of the binding interactions by about ( 5 X 104)-fold,since the equilibrium dissociation constant for APADH is about 5 pM and, as noted above, that for APAD-Pyr is about 10-lo M. (Because the chemistry of these adducts is dihydropyridine-like, we compare their dissociation constants with those for APADH rather than APAD-see also Discussion.) In addition, the presence of enzyme stabilizes APAD-Pyr, since the rate constant for decomposition of E-H-APAD-Pyr, 1 X s-l, A simple approach is used to determine whether kdscor kon controls the steady-state concentration of APNAD-Pyr; the observed rate constant, koM, for the disappearance of ESAPNAD-Pyr must be sensitive to the initial concentration of E-adduct if kOff1 k d s . The steady-state rate equation describing Scheme I1 is d[E.APAD-Pyr] = (kdcc + ko~fk~e))/(ko,[E]k:')[E-APAD-Pyrl dr When k,,,,[E] >> k:C and [E] >> k,c/k,, (Le., [E] >> KApGpr), only kdec will be significant in this equation. Likewise, when k:" >> k,[E], k o w will equal kd, + k,* (Obviously, when k,, > ESAPNADPyr remaining against time where k,,[E] >> KAPABer. The observed value for the disappearance of adduct is 1.1 X s-', and this value must approach kds in Scheme 11. Alternatively, at an initial concentration of EqAPNAD-Pyr about 10-fold larger than ~ [E] >> ICAPAwPyr), a semilog plot of the the value of K 1 , A p ~ A m e(Le., fraction of the enzyme containing adduct against time is biphasic (curve B, Figure 4). Since the value of k , ~ 7, X s-I, for the linear phase is 7-fold larger than the value of kow at high initial [E], curve A, it follows that kon must be larger than kd,, that kfc >> k,p[E], and that qp* 'v KAPNGM N M. (A lower limit for KApAbpyr of 6 X IO-" was calculated from the magnitude of the burst phase, 2 X M, in curve B as an internal test of consistency.) A similar set of experiments also was conducted with E-NAD-Pyr. With the latter adduct complex, the decomposition step kdccmust be faster than the dissociation step koffin contrast with E.APAD-Pyr (cf. the preceding paper).
e
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B I 0C H E M I ST R Y I
BURGNER AND RAY I
I
I
I
.20
~~
Table I: Estimates of the Rate Constants for the Enzyme-Catalyzed NAD-Pvr Reaction' const const k l (M-' S-I) 1 X lo7 ks (s-]) 2 X IO5 k2 6-9 3 X lo5 k6 3X k3 (M-I s-I) 30 K,"d 4 x 106 k4 (M-I s-]) 2 x 107 'The constants, which are identified in Scheme I, were evaluated in the manner described under Results from experiments at pH 7 and 15 "C. bFrom Burgner & Ray (1974). ~
~~~~~
(si1)
r
I
v .12
%
In
n x
.04
I
30
I
I
90
I
L
15
[APNAD-PYR] ,nm FIGURE5 : Effect of APAD-Pyr on the rate of approach to steady state. The conditions are the same as those for Figure 2. The line was drawn by eye, with a slope of 2.4 X lo6 M-' s-l and intercept of 0.002 s-I (see text for further details).
is about 0.07 of that observed in the absence of enzyme, 1.5 x 10-3 s-1. Estimation of the Dissociation Constant for the Complex of APAD-Pyr and LDH by Measuring the Rate Constants for the Binding and Dissociation Steps. As was shown above, product-time plots obtained with the normal enzymic assay are biphasic when the reaction is initiated by adding enzyme to an assay mixture containing APAD-Pyr-see Figure 2. When A is defined in the manner shown in Figure 2, a plot of log A against time will result that is linear for approximately 3 halftimes. Thus, the rate equation describing the approach to steady state is first order in enzyme concentration. This first-order dependence is further demonstrated by the insensitivity of the rate constant describing the burst phase, kburst, to a 10-fold change in enzyme concentration (not shown). In addition, a plot of kburstagainst [APAD-Pyr] is essentially linear (Figure 4); thus, the rate equation describing the burst phase also must be first order in APAD-Pyr. Since kburst represents the approach to steady state, kht should be related to the sum of the on- and off-rates for APAD-Pyr, after correction for the rate of the nonenzymic decompositionsee Scheme 11. Hence, kburst= &P[APAD-Pyr] + kOff k? when the [APAD-Pyr] does not change significantly (
